82.17.5 problem Ex. 5

Internal problem ID [18821]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Problems at page 37
Problem number : Ex. 5
Date solved : Tuesday, January 28, 2025 at 12:21:32 PM
CAS classification : [_separable]

\begin{align*} x y \left (y-x y^{\prime }\right )&=x +y^{\prime } y \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

dsolve(x*y(x)*(y(x)-diff(y(x),x)*x)=x+diff(y(x),x)*y(x),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \sqrt {c_{1} x^{2}+c_{1} +1} \\ y \left (x \right ) &= -\sqrt {c_{1} x^{2}+c_{1} +1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.835 (sec). Leaf size: 57

DSolve[x*y[x]*(y[x]-D[y[x],x]*x)==x+D[y[x],x]*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {1+e^{2 c_1} \left (x^2+1\right )} \\ y(x)\to \sqrt {1+e^{2 c_1} \left (x^2+1\right )} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}